The common rail supplies a number of injectors of the cylinders of the engine, and is supplied by a constant-displacement high-pressure pump in turn supplied by a low-pressure, variable-delivery, variable-pressure, motor-driven pump. The control device has an electronic control unit for receiving signals indicating operating conditions of the engine; the suction side of the high-pressure pump has a choke; and the control unit controls the motor-driven pump to vary the fuel pressure upstream from the choke between a predetermined maximum value and a predetermined minimum value, so as to regulate the fuel intake of the high-pressure pump within a predetermined range.